Question: Simplify the following expression and state the condition under which the simplification is valid. You can assume that $q \neq 0$. $n = \dfrac{7(5q - 6)}{7} \div \dfrac{q(5q - 6)}{6} $
Explanation: Dividing by an expression is the same as multiplying by its inverse. $n = \dfrac{7(5q - 6)}{7} \times \dfrac{6}{q(5q - 6)} $ When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ 7(5q - 6) \times 6 } { 7 \times q(5q - 6) } $ $ n = \dfrac{42(5q - 6)}{7q(5q - 6)} $ We can cancel the $5q - 6$ so long as $5q - 6 \neq 0$ Therefore $q \neq \dfrac{6}{5}$ $n = \dfrac{42 \cancel{(5q - 6})}{7q \cancel{(5q - 6)}} = \dfrac{42}{7q} = \dfrac{6}{q} $